Should I use bones or shape keys to control the movements of a cat models ear?
It would depend on what you want to do with the model after it was rigged. If it's going to be used in a game engine then you will want to see if it can support exported shape keys. If it will stay in Blender then shape keys will be fine. 
You can always set up both then see which works best and is easiest to do for future work.